mlsanityData to 7 Oct 2026

Nonseparable Symplectic Neural Networks

arXiv 2010.12636 ↗First posted 23 Oct 2020cs.LG cs.CE stat.MLcited by 31

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Abstract (arXiv)

Predicting the behaviors of Hamiltonian systems has been drawing increasing attention in scientific machine learning. However, the vast majority of the literature was focused on predicting separable Hamiltonian systems with their kinematic and potential energy terms being explicitly decoupled while building data-driven paradigms to predict nonseparable Hamiltonian systems that are ubiquitous in fluid dynamics and quantum mechanics were rarely explored. The main computational challenge lies in the effective embedding of symplectic priors to describe the inherently coupled evolution of position and momentum, which typically exhibits intricate dynamics. To solve the problem, we propose a novel neural network architecture, Nonseparable Symplectic Neural Networks (NSSNNs), to uncover and embed the symplectic structure of a nonseparable Hamiltonian system from limited observation data. The enabling mechanics of our approach is an augmented symplectic time integrator to decouple the position and momentum energy terms and facilitate their evolution. We demonstrated the efficacy and versatility of our method by predicting a wide range of Hamiltonian systems, both separable and nonseparable, including chaotic vortical flows. We showed the unique computational merits of our approach to yield long-term, accurate, and robust predictions for large-scale Hamiltonian systems by rigorously enforcing symplectomorphism.

Key facts. Cited by 31 papers in the map (data through 7 Oct 2026). First posted on arXiv 23 Oct 2020.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 6; 2022: 6; 2023: 1; 2024: 7; 2025: 7; 2026: 4.

31 papers.

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  1. 2021Data-driven Prediction of General Hamiltonian Dynamics via Learning Exactly-Symplectic Mapscited by 41
  2. 2021Symplectic Learning for Hamiltonian Neural Networkscited by 35
  3. 2022Deconstructing the Inductive Biases of Hamiltonian Neural Networkscited by 31
  4. 2021Which priors matter? Benchmarking models for learning latent dynamicscited by 26
  5. 2021Locally-symplectic neural networks for learning volume-preserving dynamicscited by 9
  6. 2021SyMetric: Measuring the Quality of Learnt Hamiltonian Dynamics Inferred from Visioncited by 5
  7. 2023Physics-Informed Learning Using Hamiltonian Neural Networks with Output Error Noise Modelscited by 5
  8. 2022Learning Trajectories of Hamiltonian Systems with Neural Networkscited by 4
  9. 2024Symplectic Neural Networks Based on Dynamical Systemscited by 4
  10. 2024Symplectic Neural Flows for Modeling and Discoverycited by 4
  11. 2022Bayesian Identification of Nonseparable Hamiltonian Systems Using Stochastic Dynamic Modelscited by 3
  12. 2024CLPNets: Coupled Lie-Poisson Neural Networks for Multi-Part Hamiltonian Systems with Symmetriescited by 3
19 more
  1. 2021KAM Theory Meets Statistical Learning Theory: Hamiltonian Neural Networks with Non-Zero Training Losscited by 2
  2. 2022VPNets: Volume-preserving neural networks for learning source-free dynamicscited by 2
  3. 2024Bayesian identification of nonseparable Hamiltonians with multiplicative noise using deep learning and reduced-order modelingcited by 2
  4. 2024Learning Generalized Hamiltonians using fully Symplectic Mappingscited by 2
  5. 2024Training Hamiltonian neural networks without backpropagationcited by 2
  6. 2025Rapid training of Hamiltonian graph networks using random featurescited by 2
  7. 2025Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approachcited by 2
  8. 2022Symplectically Integrated Symbolic Regression of Hamiltonian Dynamical Systemscited by 1
  9. 2022Data-driven discovery of non-Newtonian astronomy via learning non-Euclidean Hamiltoniancited by 1
  10. 2025Learning Physical Systems: Symplectification via Gauge Fixing in Dirac Structurescited by 1
  11. 2025Learning Stochastic Hamiltonian Systems via Stochastic Generating Function Neural Networkcited by 1
  12. 2025Unified Spatiotemporal Physics-Informed Learning (USPIL): A Framework for Modeling Complex Predator-Prey Dynamicscited by 1
  13. 2025Time-adaptive SympNets for separable Hamiltonian systemscited by 1
  14. 2025Time-adaptive H'enonNets for separable Hamiltonian systemscited by 1
  15. 2026Controlled oscillation modeling using port-Hamiltonian neural networkscited by 1
  16. 2026Machine Learning Hamiltonian Dynamical Systems with Sparse and Noisy Datacited by 1
  17. 2024Data-Driven Computing Methods for Nonlinear Physics Systems with Geometric Constraintscited by 0
  18. 2026Hamiltonian Graph Inference Networks: Joint structure discovery and dynamics prediction for lattice Hamiltonian systems from trajectory datacited by 0
  19. 2026Dynamical and Optimization Trade-offs of Levi--Civita Coordinates for Learned Close-Encounter Dynamicscited by 0